The Combinatorial Structure of Wait-Free Solvable Tasks

This paper presents a self-contained study of wait-free solvable tasks. A new necessary condition for wait-free solvability, based on a restricted set of executions, is proved. This set of executions induces a very simple-to-understand structure, which is used to prove tight bounds for k-set consensus and renaming. The framework is based on topology, but uses only elementary combinatorics, and, in contrast to previous works, does not rely on algebraic or geometric arguments.

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